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We propose a hierarchical modeling approach for explaining a collection of spatially referenced time series of extreme values.
We assume that the observations follow generalized extreme value (GEV) distributions whose locations and scales are jointly
spatially dependent where the dependence is captured using multivariate Markov random field models specified through coregionalization.
In addition, there is temporal dependence in the locations. There are various ways to provide appropriate specifications;
we consider four choices. The models can be fitted using a Markov Chain Monte Carlo (MCMC) algorithm to enable inference for
parameters and to provide spatio–temporal predictions. We fit the models to a set of gridded interpolated precipitation data
collected over a 50-year period for the Cape Floristic Region in South Africa, summarizing results for what appears to be
the best choice of model.
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Alan E. GelfandEmail: |
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Estimation of population size has traditionally been viewed from a finite population sampling perspective. Typically, the
objective is to obtain an estimate of the total population count of individuals within some region. Often, some stratification
scheme is used to estimate counts on subregions, whereby the total count is obtained by aggregation with weights, say, proportional
to the areas of the subregions.
We offer an alternative to the finite population sampling approach for estimating population size. The method does not require
that the subregions on which counts are available form a complete partition of the region of interest. In fact, we envision
counts coming from areal units that are small relative to the entire study region and that the total area sampled is a very
small proportion of the total study area. In extrapolating to the entire region, we might benefit from assuming that there
is spatial structure to the counts. We implement this by modeling the intensity surface as a realization from a spatially
correlated random process. In the case of multiple population or species counts, we use the linear model of coregionalization
to specify a multivariate process which provides associated intensity surfaces hence association between counts within and
across areal units.
We illustrate the method of population size estimation with simulated data and with tree counts from a Southwestern pinyon-juniper
woodland data set. 相似文献
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